Statistica Sinica 19 (2009), 197-211

CONSTRUCTION OF OPTIMAL MIXED-LEVEL

SUPERSATURATED DESIGNS

Min-Qian Liu and Dennis K. J. Lin

Nankai University and The Pennsylvania State University

Abstract: Supersaturated designs (SSDs) offer a potentially useful way to investigate many factors with only a few experiments during the preliminary stages of experimentation. While the construction and analysis of symmetrical SSDs have been widely explored, asymmetrical (or mixed-level) SSDs deserve further investigation. Mixed-level SSDs can be judged by various criteria. But, justified by existing results, the $\chi^2$ criterion proposed by Yamada and Lin (1999) is adopted here. Optimality results for mixed-level SSDs are provided. A new construction method for $\chi^2$-optimal SSDs is proposed, and we discuss properties of the resulting designs. Many new designs are tabulated for practical use.

Key words and phrases: Balanced design, column juxtaposition, Kronecker sum, orthogonal array.